Modelling Space with an Atom of Quantum Geometry

Details Modelling Space with an Atom of Quantum Geometry Modelling Space with an Atom of Quantum Geometry

2001-09-17

arxiv.org/abs/gr-qc/0109056v1

Class.Quant.Grav. 19 (2002) 2211-2228

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 11 figures

Scientific paper

10.1088/0264-9381/19/8/311

Within the context of loop quantum gravity there are several operators which measure geometry quantities. This work examines two of these operators, volume and angle, to study quantum geometry at a single spin network vertex - ``an atom of geometry.'' Several aspects of the angle operator are examined in detail including minimum angles, level spacing, and the distribution of angles. The high spin limit of the volume operator is also studied for monochromatic vertices. The results show that demands of the correct scaling relations between area and volume and requirements of the expected behavior of angles in three dimensional flat space require high-valence vertices with total spins of approximately 10^20.

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